Suppose that all the terms of an arithmetic p | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the first term be $a$ and the common difference be $d$. The sum of the first $n$ terms is given by $S_n = \frac{n}{2} [2a + (n-1)d]$.Given $\f

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(D) Let the first term be $a$ and the common difference be $d$. The sum of the first $n$ terms is given by $S_n = \frac{n}{2} [2a + (n-1)d]$.Given $\frac{S_7}{S_{11}} = \frac{6}{11}$,we have $\frac{\frac{7}{2}(2a + 6d)}{\frac{11}{2}(2a + 10d)} = \frac{6}{11}$.Simplifying this,$\frac{7(a + 3d)}{11(a + 5d)} = \frac{6}{11}$ $\Rightarrow 7a + 21d = 6a + 30d$ $\Rightarrow a = 9d$.The seventh term $a_7 = a + 6d = 9d + 6d = 15d$.Given $130 Since all terms are natural numbers,$d$ must be an integer. Thus,$d = 9$.

Suppose that all the terms of an arithmetic progression $(A.P.)$ are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is $6:11$ and the seventh term lies between $130$ and $140$,then the common difference of this $A.P.$ is

Similar Questions

If the $n$ terms $a_1, a_2, \ldots, a_n$ are in $A$.$P$. with common difference $r$, then the difference between the mean of their squares and the square of their mean is

If the $n^{th}$ term of an arithmetic progression is $3n - 1$,then the sum of its first five terms is.......

If the roots of the equation $x^3+ax^2+bx+c=0$ are in arithmetic progression,then

If the sum of $n$ terms of an arithmetic progression is given by $Pn + Qn^2$,where $P$ and $Q$ are constants,what is the common difference?

If the sum of three consecutive terms of an $A.P.$ is $51$ and the product of the last and first term is $273$,then the numbers are

Vedclass Test Series

Exam Paper Generator

Online Exam Module